Estimation of springback in double-curvature forming of plates: Experimental evaluation and process modeling

This paper presents the results obtained from a series of experiments on double-curvature forming of 300 mm square and 15 mm thick plates of type 316L(N) stainless steel to evaluate the inherent springback and also to validate finite element method (FEM) based process model developed for forming of multiple-curvature sectors of large size vessels. The experimental results show that twisting of the plate occurs during pressing, which is unavoidable in an actual forming setup on the shop floor. Twisting increases with increase in slope of the die cavity. Springback in the plate changes in an ascending order towards the centerline of the plate from the edges. The final radius of curvature (ROC) on the pressed plate after springback does not remain constant along a particular axis although the die and the punch had constant ROC along that axis because of varying constraint to opening up of the plate from centerlines to the edges. Springback also increases with reduction in the stiffness of the die and punch. The simulated plate profiles obtained from the FEM process model for multiple-curvature plate forming compared well with the experiments, the maximum error being within 6%. The process model used a sequential dynamic explicit formulation for the plate pressing phase and a static implicit formulation for the unloading (springback) phase in the Lagrangian framework. Reduced integration shell elements were used for the plate and the die and the punch were considered rigid. Dynamic explicit FEM for pressing and static implicit FEM for the unloading phase are adequate and economic for modeling of plate forming process by using FEM. The necessary material and frictional property data needed for the FEM process model were generated in-house. This model can be applied to design of dies and punches for forming the petals of large pressure vessels. The FEM process model predicts the final shape of the product and the residual cold work level for a given die, punch and plate configuration and this information can be used to correct the die and punch shapes for springback to manufacture the petals to the desired accuracy.     

中厚板轧制板坯弯曲的有限元模拟分析

建立了中厚板轧制的二维有限元模型,分析了压下率、轧辊转速比、板坯初始温度、板坯厚度方向的温度差以及电机的加速制度等对板坯弯曲的影响。这些分析结果对控制板坯弯曲提供了一定的理论依据。     

The perforation of circular plates with four-sided pyramidally-headed square-section punches

Circular plates of mild steel, brass, copper and aluminium were perforated normally from one side by square section punches possessing pointed pyramidal heads of semi-angle 15, 30, 45, 60, 75 and 90° and corresponding punch load-displacement curves are presented. The distinctly different characteristics of petalling and plugging modes of deformation are demonstrated and related to punch semi-angle. The onset of fractures leading to petalling is described and particular attention is drawn to the curly petal (as opposed to the straight petal) found with small angle punches.

Among other interesting features of this process a common characteristic curve and magnitude of parameter—equal to the maximum load during penetration divided by tensile strength—is shown to prevail for all materials over the whole range of punch angles. For the punch side length to plate thickness ratios 4:1 and 8:1, as with conical and ogival punches, the punch semi-angle 45° is found to be (about) the angle of changeover from petalling to plugging modes.     

圆柱滚子轴承实体保持架兜孔锁点爪劈压加工工艺

采用手锤敲击冲子劈压保持架锁点爪时不能有效控制冲击力大小及方向,限定了锁点爪劈压状态的一致性,圆柱滚子轴承装配中常产生滚子从保持架掉出或内圈无法组装的情况。通过优化保持架锁点爪劈压加工工艺,采用单柱液压机并配套设计劈压工装,使保持架锁点爪劈压加工时所受压力恒定,劈压后锁点爪状态稳定、可控,满足轴承装配质量要求。     

Model for the Whole Roller Leveling Process of Plates with Random Curvature Distribution Based on the Curvature Integration Method

A model based on the curvature integration method has been applied in an online plate leveling system. However,there are some shortcomings in the current leveling models. On the one hand, the models cannot deal with the leveling process of plates with a random curvature distribution. On the other hand, the current models are suitable only for stable leveling processes and ignore the biting in and tailing out stages. This study presents a new plate-leveling model based on the curvature integration method, which can describe the leveling process of plates with random curvature distribution. Further, the model is solved in two cases in order to take the biting in and tailing out stages into consideration. The proposed model is evaluated by comparing with a plate leveling experiment. Finally, the leveling process of a plate with a wave bent is studied using the proposed model. It is found that the contact angles vary greatly during the biting in and tailing out stages. However, they are relatively steady during the 5 roller leveling stage.In addition, the contact angle of roller No. 2 is the smallest, which is close to 0. Roller leveling can e ectively eliminate bending in the plate, but there are regions in the head and tail of the plate, where roller leveling is not e ective. The non-leveling region length is about 2 times that of the roller space. This study proposes a quasi-static plate-leveling model, which makes it possible to analyze the dynamic straightening process using a curvature integration method. It also makes it possible to analyze the straightening process of a plate with random curvature distribution.     

基于粉末本构模型和多体力学仿真的模架集成式粉末成形设备的设计

研制出一种新型的低成本、小体积、高精度的专用模架集成式粉末成形设备。以MSC.Marc与MSC.Adams软件相结合提出基于数值模拟的1 MN压机设计方法,即根据粉末压制试验构建末材料流动应力本构模型;通过该模型在MSC.Marc软件数值计算出所设计压机压制过程的模冲载荷;在分析模架集成式粉末成形设备各个模板在压制工过程运动特点的基础上,建立多体运动学数学方程;将所得模冲载荷作为边界条件加载到对模架集成式粉末成形设备在压制过程的模拟仿真;并在MSC.Adams软件中分析各个模板在压制过程中力学状态,从中分析该设备在实际工况下的可靠性。研制出电液比例阀和光栅尺相结合的控制系统,实现对缸同时驱动,解决不同模板之间的动作协调的问题,所研制试验样机实现零件轴向压制精度为±0.02 mm。实际压制过程所得各模冲载荷与模拟结果相一致,从而验证粉末成形设备设计所采用的本构模型是准确的,基于数值模拟进行粉末成形设备设计的方法的正确性。     

Investigation of sheet metal forming by bending—Part IV: Bending and wrinkling of circular sheets pressed by a hemispherical punch

This paper reports on an investigation of the bending forming processes in circular sheets pressed by a hemispherical punch into a conical die. Both theoretical and experimental considerations are provided. It is pointed out that the deformation mechanism of such a circular plate is different from that of the workpiece in the conical die cup test studied previously in part III of this series [Int. J. Mech. Sci.31, 327–333 (1989)]. The theoretical analysis shows that a central gap appears between the plate and the hemispherical punch at small deflections and disappears when the punch force increases beyond a certain magnitude. It is then shown that the previous approximate analytical treatment of the distribution of punch force is no longer appropriate to the wrinkling of the plate. It is shown that, as in the case of the conical die cup test, the circumferential wave number for the wrinkling mode corresponding to the critical wrinkling load of the present workpiece is four. In addition, the paper reveals that a doubling of the wrinkling wave may occur in the first stage of the forming process.     

Influence of axial force on the elastic-plastic bending and springback of a beam

In the industrial forming of metal sheet or plate components by means of a bending operation, a constant problem is the change of shape, or “springback”, of the formed part under the elastic stresses that are released when the forming pressure is removed. For the close-tolerance forming of such components, an accurate means of calculating the springback is of great value, as this enables a corrective allowance to be made when designing and performing the forming operation itself. In the present paper, the influence of axial force on the elastic-plastic bending and springback of a beam is examined. After obtaining the fundamental relationship between the curvature of the beam and the load for the case of pure bending, both the elastic-plastic bending of a cantilever subjected to a concentrated force at its tip and the springback are considered. It is shown that the analysis can be applied to the press-brake bending of strips and the equibiaxial bending of plates.     

Tribological properties of asperity arrays coated with self-assembled monolayers

The effects of a self-assembled monolayer (SAM) coating on the friction and pull-off forces were determined by using two-dimensional asperity arrays on silicon wafers. The arrays were coated with SAM composed of one of five different alkylchlorsilanes. First, two-dimensional asperity arrays were created by using a focussed ion beam (FIB) system to mill patterns on silicon plates. Each silicon plate had different patterns of equally spaced asperities. Each pattern (5 × 5 μm²) had a different radius of curvature of the asperity peaks, ranging from about 200 to 2500 nm. Then, each silicon plate was immersed in a solution of a different alkylchlorsilane in hexane (either hexyltrichlorosilane, octyltrichlorosilane, dodecyltrichlorosilane, tetradecyltrichlorosilane, or octadecyltrichlorosilane), thus coating the asperity arrays with SAM. The friction and pull-off forces on the SAM-coated arrays were measured by using an atomic force microscope (AFM) that had a square flat probe. The pull-off force for SAM-coated silicon was roughly proportional to the radius of curvature of the asperity peaks. The magnitude of the pull-off force corresponded approximately to the capillary force calculated by using the contact angle of water on the surface of SAM. The friction coefficient correlated with the inverse of the alkyl-chain length of the SAM.     

侧向槽粉末制品压制成型工艺

叙述了YAN79Z-B型模架全自动干粉成型液压机压制工艺的设计，在压制粉末冶金侧向槽过程中，阴模与浮动冲上升到设定位置，送粉器前移对阴模腔内充满粉料后，上冲下行到阴模内向下压制时，利用阴模与浮动冲的同步浮动，压制到终了位置产品成型，然后阴模拉下，浮动冲微升推出产品，实现了侧向槽产品国产化，自动化生产。     

Fabrication of micro-channel arrays on thin stainless steel sheets for proton exchange membrane fuel cells using micro-stamping technology

Bipolar plates are one of the crucial components of proton exchange membrane fuel cells. Because of the expensive production costs of traditional graphite bipolar plates, which require a few millimeters thickness over the space, the resulting metal bipolar plate reduces the cost, and the thickness can be reduced to the micron range. This study explored the application of micro-stamping technology to produce thin metal bipolar plates with the relevant process parameters. In this study, the channel design was 0.8?×0.75 mm for the use of a rigid punch on a 50-μm-thick stainless steel sheet (SUS 304) for micro-channel stamping processes. The finite element method and the experimental results were used to analyze the main parameters of the micro-stamping process. The traditional material model and the scale factor modified material model were used for simulation. The experimental results verified that the modified material model is more realistic for products and has superior similarity because the punch load is relatively small. This study used updated Lagrangian formulation concept to establish an elastic–plastic deformation finite element analysis model and scale factor to modify the calculation to effectively simulate the micro-stamping process for metal bipolar plates.     

轴承套圈锻造过程的计算机仿真研究

本文运用MSC-Marc软件对轴承锻造加工过程进行了计算机仿真.以金属成形理论和有限元方法基本原理为基础,建立了热力偶合刚粘塑性轴承锻造模型.包括对材料特性进行了完整的描述,确定了成形模拟中体积不可压缩实现方法.以二代轮毂轴承外圈锻造为例进行模拟分析.模拟分析中进行了冲头力的计算及对两次预成形模型的实验和模拟结果的对比;提出了产生过大冲头力的一个原因是最终成形阶段工件在模腔内分布不均使变形速率急剧增加;分析了工件应力和模具结构的关系及其优化问题,对冲头的倒角圆弧半径作了优化;对温度效应、表面质量和金属流线等锻造设计有关问题作了讨论.提出了预成形坯的设计优化准则,以此设计了二代轮毂轴承外圈的优化的预成形结构,冲头力比原设计下降了一半以上.     

Fracture prediction of thin plates under hemi-spherical punch with calibration and experimental verification

The response of thin clamped plates subjected to static punch indentation is investigated experimentally, analytically and numerically to determine the onset of fracture. The accumulated equivalent plastic strain with stress triaxiality as a weighing function is introduced as ductile fracture criterion in the finite-element simulation and analytical prediction. The fracture criterion was calibrated by finite-element simulations of uniaxial tensile tests. Based on the calibration, and calculated distributions and histories of stress and strain, the critical location, and penetration to fracture were predicted within 5–10% accuracy for three punch radii.The plots of force–penetration and locations of fracture initiation in the static punch indentation tests were compared with finite-element simulations and analytical approximations showing good agreement. The transverse deflection profiles of the plates at the point of fracture obtained numerically were shown to agree well with the closed-form solution derived by taking into account a variable stress ratio and varying stress triaxiality. The strain distribution along the plate radius is influenced by the friction between the interfaces of punch and plate. By changing the friction coefficient, the fracture-forming limit diagram was constructed numerically. The present procedure can replace the time-consuming experimental technique in which the strain path is controlled by changing the radius of a cut off.     

Large deflexion of plates with initial curvature

The dynamic relaxation method is used to study the large deflexion of plates with small initial curvature. Details of the numerical techniques are presented with special reference to the boundary conditions. The method is used to analyse the large deflexion of square plates with a lateral load on the concave face; the initial deflexions vary from 0·1 to 5·0 times the plate thickness. A second problem is concerned with the postbuckling of plates having initial deflexions. Both square and rectangular plates are considered with the initial deflexions varying from 0·1 to 2·5 of the plate thickness.     

Prediction of bend force and bend angle in air bending of electrogalvanized steel using response surface methodology

This paper presents the development of predictive models for bend force and final bend angle (after springback) in air bending of electrogalvanized steel sheet employing response surface methodology. The models are developed based on five-level half factorial central composite design of experiments with strain hardening exponent, coating thickness, die opening, die radius, punch radius, punch travel, punch velocity as input parameters and bend force and final bend angle as responses. The results obtained from the models are in good accord with the experimental results. The effects of individual parameters and their interactions on the responses have also been analyzed in this study.     

Pressing of a thin-wall tube by a curvilinear matrix

A model of pressing a thin-wall tube by a curvilinear matrix taking into account the strengthening, normal anisotropy, change in the wall thickness, and contact friction according to the momentless theory of a rigid-plastic shell with a quadratic plasticity condition is elaborated. The calculation program of this model determines the distributions of the thickness, meridional stress, contact pressure, and fluidity stress of the strengthened material along the generatrix of the deformed tube and the plot of the change of the pressing force, depending on the displacement of the punch.     

Effect of forming conditions on linear patterning of polymer materials by hot embossing process

In this work we demonstrate the hot-embossing process under different forming conditions such as forming temperature, load, and holding time in pressing, in order to determine the suitable conditions required for linear patterning on polymer plates (PMMA and PC). Results showed that the replicated pattern depth increased in proportion to an increase in the forming temperature, load, and time. The reduction of the workpiece thickness increased according to the holding time in the pressing process. In the process of time, the reduction ratio of the workpiece thickness decreased due to the surface area increment of the workpiece, while the pressure on the workpiece declined. In order to reduce the bulging ratio we introduced a temperature difference between the upper and the lower punch.     

A new model for the plate leveling process based on curvature integration method

Leveling is a process used to minimize the plate defects including flatness imperfections and uniformity of internal stress in the plate industry. It plays an important role in delivering the desired material properties and product standards required. This paper presents a new mechanics model for predicting the leveling process of plates. First, the mechanics model is developed based on the curvature integration method. Next, a global nonlinear unconstrained optimization method is utilized to solve this model. Then, the presented model is evaluated by comparative study to experimental data. Finally, the leveling process is studied using our model. It is found that the bending curvature of the plate is highly sensitive to the contact angles between the plate and the roller. The defective plate with different initial curvature tends to be flatted and the residual stress can be reduced effectively after being leveled.     

Influence of piezoceramic to fused silica plate thickness on the radii of curvature of piezoelectric bimorph mirror

Piezoelectric based bimorph mirrors (PBM) find extensive use in focusing of x-ray beams. Many optical instruments require use of PBM whose radii of curvature can be tuned precisely. The 100 mm and 300 mm PBMs were fabricated with varying piezoelectric to fused silica plate thicknesses. The radii of curvature of free standing mirrors were measured as a function of voltage and it was found to decrease with increasing voltage. For a given piezoelectric plate thickness, as the fused silica thickness increases, the radii of curvature was found to increase owing to increase in stiffness of the mirror. On the other hand, for a given fused silica plate thickness, when the piezoelectric plate thickness is increased, the radii of curvature are decreased for a given electric field, due to increase in generated force. This study brings out the influence of piezoceramic to fused silica plate thickness on the radii of curvature of PBM.